Abstract:

The efficiency of instructional methods is not universal but depends on the desired outcomes and the instructional conditions (Reigeluth, 1999). According to Hannafin (1996), sometimes direct instruction is not the best method to support learning. This statement opens the door for alternative teaching/learning methods. Open learning environments (OLEs) can contribute to meet the goals and challenges of (mathematics) education. This is one of the reasons to survey how mathematics teachers tackle some specific instructional choices, such as the use of OLEs to support problem solving processes in mathematics.
This survey examines mathematics teachers’ acceptance (in the sense of approving its utility in teaching/learning mathematics and teachers’ willingness to implement it) of the notion of computer supported-OLE (CS-OLE) as method for teaching the students to solve problems and its relationships with teachers’ beliefs on the nature of mathematics (NM), mathematics teaching (MT), and technology as a mathematics teaching tool (TMTT). In this research, we adopt the framework on teachers’ beliefs proposed by Philipp (2007) and Thompson (1992).
The present study focuses on teachers’ beliefs about NM and MT, because they have been argued to specifically affect teachers’ approaches to mathematics teaching. Since computers have a significant function in CS-OLEs, we also focus on teachers’ beliefs about TMTT.
This research is based on:
-Ernest’s theory of views of NM (1989, 1991): instrumentalist, Platonist, and problem solving;
-the study of Kaiser (Kaiser, Hino, & Knipping, 2006) on central orientations of teaching in mathematics education, classifying beliefs about MT into two categories with contrasting peculiarities: scientific versus pragmatic understanding of mathematics theory;
-the technology acceptance model (Davis, 1989), also applied in educational studies about curricular domains (Stols, 2007; Teo, 2009).
-the model of OLE developed by Clarebout (2005), which integrates the main features of the OLEs given by influential researchers (Hannafin, Hall, Land, & Hill, 1994; Jonassen, 1999).
The survey reached the teachers working in 36 Italian first degree secondary schools. In Italy, the situation of mathematical education (particularly about problem solving) is in peril (see the results of PISA and TIMSS surveys), in spite of the guidelines given by the European Union.
Data about teachers’ beliefs and their acceptance of CS-OLE were collected through a Likert-scale based questionnaire including a set to survey TMTT proposed by Davis (1989) and two sets to survey NM and MT proposed by Yu (2008a, 2008b, 2009). His study refers to Ernest’s classification of NM and to beliefs on MT based on the conception of mathematics education by Kaiser et al., (2006).
The reliability of the scales to measure beliefs was studied and the subsequent factor analyses resulted in some new scales. Since multiple factors were interrelated, multivariate analyses of variance were executed with acceptance of CS-OLEs as independent variable.
Empirical evidence was found supporting the hypothesized relationships among teachers’ acceptance of the notion of CS-OLE and their beliefs on NM, MT and TMTT. These findings may help to solve some serious actual difficulties with respect to mathematics education in Italy, mainly concerning students’ handling of mathematical problem solving (e.g. through improving pre-service and in-service teacher education).

Keywords:

Computer supported learning environments, mathematics education, problem solving, teachers’ beliefs.